Metallic structure for delaying propagated waves



L-IU IIIIII vs.

W. E. KOCK Dec. 18, 1951 METALLIC STRUCTURE FOR DELAYING PROPAGATED IAVES Filed lay 16, 1947 6 Sheets-Sheet 2 INVENTR 5. KOCK TRANSLATION AT T QRNE Y W. E. KOCK Dec. 18, 1951 METALLIC STRUCTURE FOR DELAYING PROPAGATED WAVES Filed lay 16, 1947 6 Sheets-Sheet 3 FIG/7 TRA MLA TION rl a OWN-U050 1 m m M m x a w 3 c fiwfiuui 9 mm m 1., m J w F n "M l m D D DEGREE 0F AXIS INVENTOR W. E. K OCK BY a ATTORNEY Dec. 18, 1951 w, KOCK 2,579,324

METALLIC STRUCTURE FOR DELAYING PROPAGATED WAVES Filed lay 16, 1947 6 Sheets-Sheet 4 FIG?! 7R4 NSLATDN DEV/CC INVENTOR W E. KOCK A T TOR/V5 Y LAHHHNKH Dec. 18, 1951 w. a. KOCK 3 METALLIC STRUCTURE FOR umvmc PROPAGA'I'ED Was 5) Filed lay 16. 1947 s Sheets-Sheet 5 TRANSLAWON DEVICE INVENTOR W. E. KOCK ATTORNEY Dec. 18, 1951 w. KQCK 2,579,324

IETALLIC STRUCTURE FOR DELAYING PROPAGA'I'ED IAVES Filed lay 16, 1947 6 Sheets-Sheet 6 I62 16:1l I6! 165 F a 2 TRANSLA T/ON DEVICE FIG. 29

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g 1.: E I73 3 Lo H 440a 0000 an uoa ram. m uses. w

us no no a. luvnzucru in ms.

INVENTOR m E. KOCK .4 T TORNE V Patented Dec. 18, 1951 UNITED STATES PATENT OFFICE METALLIC STRUCTURE FOR DELAYING PEOPAGATED WAVES Application May I6, 1947, Serial No. 748,447 8 Claims. (Ci. 250-3353) This invention relates to passive devices for changing the phase velocity of electromagnetic waves and, in particular, to radio refractors designed for use in directive and non-directive antenna systems.

As is known, metallic-dielectric phase velocity changers comprising iron conductors immersed in a solid dielectric substance have been suggested for generating short radio waves (10-185 meters) and an end-on array of passive wires H) or directors spaced in the air dielectric medium has been proposed for directively propagating short radio waves. Also, solid dielectric delay, or so-called velocity-decrease, refractors of the focussing and non-focussing types, have been proposed for changing or bending the propagation direction of radio waves. Thus, Patent 706,739 granted to R. A. Fessenden on August 12, 1902, discloses a metallic-dielectric short wave generator; Figs. 1 and 4 of Patent 1,860,123

granted to H. Yagi on May 24, 1932, discloses an end-on array of passive wires, and Fig. 21 of Patent 2,283,935 granted to A. P. King on May 26, 1942, illustrates a horn antenna having a solid dielectric delay lens in its mouth orifice. addition, as disclosed in my copending applications, Serial Nos. 642,722 and 642,723, both filed on January 22, 1946, metallic-advance lenses comprising air dielectric channels have been sug- 2 dielectric and solid dielectric structures are relatively heavy and difflcult to manufacture. Moreover, the attenuation of the waves passing through these structures is considerable. In

5 addition, in the case of the solid dielectric lens,

the amount of reflection at the two surfaces of the dielectric material, is usually fairly high, with the result that the total energy loss is appreciable and the directivity gain of the lens is not relatively high. On the contrary, the aforesaid metallic-advance lenses are lightweight and substantially lossless; and the directivity gain is high, that is, considerably greater than that of the solid dielectric lens. Accordingly, it now appears desirable to obtain refractors, and particularly lenses, which possess the advantages, but are devoid of the disadvantages, inherent in the above-mentioned prior art structures. In particular, it appears desirable to obtain a metallic lens having distinctive attributes not found in the lenses and other structure heretofore utilized.

It is one object of this invention to alter the phase velocity of an electromagnetic wave in a more emcient and satisfactory manner than heretofore accomplished.

It is another object of this invention to refract radio waves in a more efficient and satisfactory manner than heretofore accomplished.

g ested for use in very-short wave (1-10 meters), It is another object of this invention to focus, ulwsficrrt'-wave-+1o-100 centimeters) and with only ne l gible loss, electroma net c waves super-short wave or microwave (l-ib cenu--- included in an exceeding y e band of Wavemeters) antenna systems. lengths.

In general, the solid dielectric delay lens is It is another object of this invention to obisotropic; and since the dielectric constant, and tain, in a metallic lens, a high gain, broad band therefore the refractive index, of the delay lens do not vary appreciably with frequency, in the frequency region in which they are employed, the lens has a relatively broad band width. On the other hand, the end-on array mentioned above is 40 frequency sensitive since the wires are only slightly shorter than one-half the operating wavelength. a narrow may designed for two polarizations, ordinarily these lenses are suitable for utilization with only a single polariza- 'tion.

The.metallic-advance refractors have, however, distinct advantages not found in the metallic-dielectric phase velocity changer or the isotropic or uasi-isotropic characteristic.

It is still another object of this invention to obtain, in a refractor a refractive index eater or smaller than unity, dependent upon the frequency o refractor. It is a further object of this invention to obtain a broad band refractor which, as compared ma (1 refractors heretofore utilized, is lighter, more easily constructed and less expensive.

- In accordance with one embodiment of the invention a metallic-delay assembly or array for refracting radio waves comprises small spherical conductive elements having diameters of about three-eighths of an inch and spaced, center to center, about three-fourths of an inch apart and along three dimensions in a dielectric medium or binder, such as polystyrene foam.

e wave propagated through the solid dielectric lens. Thus the priorartmetallic- The diameter of each sphere, and hence the ,jh wag e The effective dielectric constant Bi" the three dimensional array of conductive elements is a function of the polarizability of a typical individual element and the number of elements dispersed in a unit volume of the structure comprising the foam and the array; and it is greater than unity. Hence the refractive index of the structure is greater than unity so that, in operation, the structure functions to delay or retard the phase velocity of the waves propagated therethrough. The metallic delay structure is truly isotropic inasmuch as for all possible E vector directions, and therefore irrespective of the wave propagation direction, a diameter of each sphere is aligned with the E vector. In one embodiment the structure is shaped so as to constitute a plano-hyperbolically convex diverging or positive lens. In another embodiment, the structure is shaped like a prism.

In still another embodiment of the invention,

thin conductive disks are used in place of the conductive spheres described above, the flat disk sides extending in the plane of the wave front and the thickness dimension being perpendicular to the E vector. The disk Wpe of metallic-delay structure is anisotropic. In one sense, however, it is quasi-isotropic since the diverse diameters of each disk are parallel only to the diverse possible E polarization directions included in plane of a wave front extending parallel to the disk faces, the wave front being, of course, perpendicular to the wave propagation direction aligned with the optical axis of the structure. T h e embodiment comprising disks is usually preferred over the embodiment comprising spheres because, in contrast to the spherical-elements, the thin disk elements d iahly v... he magnetic lines cf torce and ence do not dee, e a y, the expected or theoretical value of the refractive index.

If desired, instead of polystyrene foam, a dielectric medium, such as air, vacuum or rubber, may be utilized in the metallic delay structure. If the dielectric constant of the medium is not negligible, the over-all efi'ective dielectric constant of the refractor is dependent upon the proportions, by volume, of the medium and of the conductive array in a unit volume of the refractive structure.

The conductive spheres or disks in the abovedescribed embodiments may, for purpose of explanation, be considered as linear capacitative elements aligned with and spaced along the E vector, and also spaced along the propagation path. Hence, in a sense, they constitute shunt capacitors for loading free space in a manner such as to effect a reduction in the phase velocity of the space wave. Analogously, shunt condensers on a transmission line act as loading elements and function to reduce the wave velocity.

In addition, other embodiments comprising linear wire elements, tilted rod elements and square mote or dot elements of; are described and claimed here Also, it may be added, other types of metallic-delay structures, such as wave changers and lenses comprising solid or grid metallic strips, are disclosed and claimed in my copending application for "Transmission Systems, Serial No. 748,448, filed on May 16, 1947 concurrently with the present application.

The invention will be more fully understood from a perusal of the following specification taken in conjunction with the drawing on which like reference characters denote elements of similar function and on which:

Figs. 1 and 2 are explanatory diagrams used in explaining the invention;

Fig. 3 is a perspective view, and Figs. 4 and 5 are respectively, front and side views, of a metallic-delay structure constructed in accordance with the invention;

Fig. 6 is a side view of another metallic-delay structure constructed in accordance with the invention;

Figs. 7, 8 and 9 are also explanatory diagrams used in explaining the invention;

Figs. 10 and 11 are, respectively, perspective and side views of an isotropic metallic-delay prism constructed in accordance with the invention;

Figs. 12 and 13, are, respectively, perspective and side views of a directive antenna system comprising an isotropic metallic-delay, circularly symmetrical, lens constructed in accordance with the invention;

Figs. 14 and 15 are, respectively, perspective and side views of an antenna system comprising another isotropic metallic-delay, circularly symmetrical, lens constructed in accordance with the invention;

Fig. 16 is a side view of an antenna system comprising a quasi-isotropic metallic-delay, circularly symmetrical, lens constructed in accordance with the invention;

Figs. 17 and 18 are, respectively, front and back views of the lens included in the system of Fig. 16, and Fig. 19 is a directive pattern of the system of Fig. 16;

Fig. 20 is a side view of an antenna system comprising another quasi-isotropic metallicdelay, circularly symmetrical, lens constructed in accordance with the invention;

Figs. 21, 22 and 23 are, respectively, a tilted front view, an exploded perspective view and an enlarged detail partial side view of the lens utilized in the system of Fig. 20;

Fig. 24 is a perspective view of an antenna system comprising a quasi-isotropic metallic-delay, cylindrically symmetrical, lens constructed in accordance with the invention, and Fig. 25 is an exploded perspective view of the lens used in the system of Fig. 24.

Fig. 26 is a side view of an antenna system comprising an isotropic circularly symmetrical, frequency sensitive, metallic-delay or metallicadvance lens constructed in accordance with the invention; Figs. 27 and 28 are enlarged partial side and front views, respectively, of the lens used in the system of Fig. 26, and Fig. 29 is a dispersion curve for the lens of Fig. 26.

Before describing the several embodiments of the invention illustrated on the drawing, the theory underlying the metallic-delay structures will be discussed. Referring to Fig. 1, reference numerals I and 2 denote, respectively, oppositely polarized unit or point-charges +q and --q, which are displaced from each other a minute LIU'HHHELEE distance and which constitute an electric dipole; and numeral 3 denotes the electric vector connecting the charges and having a length ds. The electric dipole moment, m, is defined as fi=q 3's (1) The potential, V, at any point. 11. resulting from a point-charge, q. is defined as the work required to move a unit charge from infinity to that point,

41rer i (2) where r is the distance from the point in question to the charge q, and e is the dielectric constant. If there are several charges present. their fields can be superposed and the potential is given by where 1+ and rare, respectively, the distances from the point p to the positive charge +q and the negative charge a. and Va is the electric dipole potential. As indicated in Fig. l

or, from Equation Llhe potential distribution of a dipole of moment m is ml 4 I irer g Referring to Fig. 2, reference numeral 4 denotes a homogeneous dielectri c medium 4 in which a uniform electrostatic field E exists, the polarization of the field being represents by the arrows 5. The impressed field E causes a redistribution, that is, a displacement or realignment, of the charges or charged particles in the field, and causes them to simulate electric dipoles.

It may be well to point out here that the dielectric mediumor material is assumed to be a non-polar" or hetero-polar dielectric containing molecules which have charges, but no electric dipole moment until an electric field is applied. The polarization of such materials, and the artificial dielectrics considered herein, is accordingly independent of temperature. Onthe other'hand so-called polar dielectrics have arrangements of charged particles which are electric dipoles even before an external electric field is applied.

The applied field tends to align these dipoles and collisions produced by thermal motion tend to destroy the alignment. Accordingly, the amount of polarization, and hence the dielectric constant, which the particles exhibit depend upon the temperature.

The density of thelines of force, Fig. 2, of the displacement vector D will be e times as great as the density of the lines of force of the 1 3 vector. Now, let us remove a right cylindrical section G of 6 the dielectric, the section 6 having its axis parallel to E, and let us place positive and negative charges at the ends of the space previously occupied by the removed cylinder, in a manner such that the field is not disturbed. Inside the empty space fim=afi (10) whereas, outside the cylindrical space 5out=ei=5, as before (11) where an and e are, respectively, the dielectric constant of free space and the dielectric constant of the dielectric medium. Now, a charge +q and q placed, respectively, on the plates of a parallel plate air condenser of unit area will produce between the plates a field having a magnitude Similarly, the field inside the cylindrical space, and resulting from the added charges q per unit area at its ends, will have a magnitude E, as given by Equation 12. Since we postulated that the field be not disturbed coE' must equal the difference between Dout, Equation 10, and EOE, that is,

where er is the relative dielectric constant so that The cylindrical element 6 has at each transverse end an area 8, and charges +qs and qs at its ends. Hence, from Equation 1 we have dm. is the electric dipole moment of the cylindrical space dl is the length of the cylinder.

From Equations 16 and 17 we have dE= e-1 .0 Esdz (is) But sdl=d1 (19) so that d 77 l=(er1)ee E 7 a (20) where d:- is an element of volume.

The electric dipole moment d5, referred to a unit volume of the medium, is defined as the polarization, 5 of the medium, and we have =(a-imi (22) Referring now to Figs. 3, 4 and 5, reference numeral I denotes a wave delay structure or device comprising a dielectric medium 8, such as air or polystyrene foam and conductive objects 9 as, for example, metallic linear elements spaced along the three dimensions X, Y and Z of the medium 8. The elements 9 form a metallic array or assembly I, or so-called artificial dielectric; material, for delaying the phase velocity of electromagnetic waves. Numerals II and I2 denote a arrows representing, respectively, the electric But polarization and the direction of propagation of the applied electric field E; and numerals l3 and II designate, respectively, the plane of the incoming wave front and the vertical plane of wave propagation. In the direction of the electric vector II, the dimensions of the elements 9 are chosen so as to be small relative to one-half of the minimum wavelength in the propagated band, that is, amut a guarteg and preferably a much anally fraction of the afores ai d wavelength, in order to avoid regnapt egegts which may occur when the element length or dimension parallel to the E vector is in the vicinity of one-half wavelength. The center-to-center spacings Sx, Sy and S, of the elements 9, along the three dimensions or axes X, Y and Z are preferably equal and less than one wavelength. The spacings between adjacent elements, each of which, as explaih'edbelow, constitutes an electric dipole, should in any event be greater than the so-called breakdown yghgor inotherwordsrsufiiciently'greattopfievent short-circuiting of the elements or dipoles. Moreover, as discussed below, the minimum spacings between the elements may, if desired, be

chosen so astdg oid mutual effects or cou ling among the elementmg'tfie elements are dispersed linearly, as illustrated in Fig. 3, the spacings of the elements are dependent upon the selected number of elements per unit volume of the structure 1.

An impressed electric field E having a polarizatlon II and a propagation direction l2, produces a redistribution of the charges on the conductive elements 9 and causes them to act like small electric dipoles. Each of these dipoles then possesses a certain electric dipole moment which is related to the impressed electric vector and the polarizability of the individual element 9 by the equation where 7n is the electric dipole moment, a is the polarizability of the individual element I and E is the impressed electric vector.

Assuming there are N elements per unit volume of the dielectric medium 8,

where F is the polarization, referred to a unit volume, of all the elements 9, that is, of the array III, as immersed in the dielectric medium 8 having a given total volume XYZ. But, from Equations 11 and 21 TEE-mi (25) so that,

D=F+eoE (27) and from Equations 24 and 27 we have B=(eo-l-Na) E=eE (2a) where is the eflective dielectric constant of the artificial dielectric material or conductive structure l0 comprising all of the elements 8.

a is, as before, the dielectric constant of free space, and

nis the relative dielectric constant.

,sim esnn where n is the refractive index of the conductive array of elements 9.

Also from Equations 28 and 29, assuming the eifective relative permeability n of the structure lltobeunity,wehave Hence, if the element polarizability, a, is known. the refractive index, n, of the structure In may be determined. The theoretical and measured polarizabilities, and the method of determining the theoretical polarizabilities, are given hereinafter. It should be pointed out that Equation 30 applies, strictly speaking, only when the elements 8 are suillciently far apart that their mutual eifects are negligible. In general, the mutual eifects are negligible, substantially, when the spacing between the elements is of the same order of magnitude as the size of the elements. Moreover, while the mutual effects may slightly alter the value of the refractive index, these effects are ordinarily not especially detrimental. If the mutual effects are not negligible, the so-called Clausius-Mosotti Equation 31 given below may be substituted under certain conditions for Equation 30.

For the conditi n of m ut1 ial interaction among 7 TE Elation 31 is more exact or rigorous Equation 30, because in Equation 31 the value of the field, acting on and tending to polarise the elements, includes not only the incoming or impressed field E, but also the local field produced by the surrounding polarized elements. On the other hand, in Equation 30, the va l ue of the field includes only the impressed field E. In deriving Equation 31 the assumption is made that the elements are arranged in an array having, as in the preferred arrangements of the structures disclosed herein, three-dimensional symmetry.

From Equation 30 we have Now, for metallic objects or elements, a is positive, as explained hereinafter. Hence the refractive index of the conductive array It! is greater than unity. Moreover, assuming the medium 8 is air or polystyrene foam, the refractive index of the array in, taken by itself, is substantially the same as the refractive index of the structure 1, since the dieletric constant of air is unity and therefore negligible, and the dielectric constant of the polystyrene is substantially unity, as explained in my copending applications mentioned above.

Also, since no and M are, respectively, greater than or and A1 because, as given in my aforesaid copending applications,

9 where on and M are, respectively, the phase velocity and wavelength of the waves in free space, and m and A1 are, respectively, the phase velocity and wavelength of the waves propagated through the medium 8 and the metallic structure Ill.

If the dielectric medium 8 is hard rubber, or some similar substance having a dielectric constant Em substantially different from unity, the overall dielectric constant ec, of the modified structure, comprising the medium or filler just mentioned and the conductive, array, may be determined from the relation 108' c=ke log e+km log em. (35) where la and km are the volume proportions, in per cent. occupied by the conductive structure and the medium, respectively, in a unit volume of the modified structure.

In determining the refractive index of the modified structure comprising a dielectric substance having a dielectric constant substantially difierent from unity, the value of cc as determined from Equation 35 should be substituted for the term t appearing in Equation 29.

It is thus apparent that the structure of Figs. 3, 4 and 5 is a delay or artificial dielectric structure for retarding the phase velocity of the waves. As previously stated, the small conductive elements 9 may be regarded as capacitive elements which load free space. Analogously, shunt capacitors on a two-wire transmission line function to reduce the wave velocity. To continue, in the case of a charged parallel plate air condenser, the capacity may be increased by inserting between the plates either solid dielectric material or insulated conducting objects, provided the objects or elements each have an appreciable length in the direction of the electrostatic lines of force, that is, in a direction perpendicular to the plates. Assuming solid dielectric material is inserted, the increase in capacity is caused by the shift, produced by the applied field, of the oppositely charged particles comprising the molecules of the solid material. If metallic elements are inserted, the elements cause rearrangement of the lines of force, and a consequent increase in the number of lines, similar to the rearrangement caused by the shift, mentioned above, of the oppositely charged particles. Hence the conductive elements 9, Fig. 3, may be considered as segments of individual condensers or as objects which, under the action of the applied field, function as electric dipoles and produce a dielectric polarization comparable to that resulting from the rearrangement of the charged particles comprising a non-polar dielectric. Either viewpoint or theory explains satisfactorily the delay action observed in the operation of the metallic structure of Fig. 3, and in the focussing operation of the artificial dielectric lenses to be described herein.

In accordance with Equation 32, the refractive index of the conductive structure 9, Fig. 3, is directly proportional to the number N of elements 9 per unit volume of the structure. Accordingly, the refractive index, and incidentally the capacity and efiective dielectric constant, may be increased by staggering the elements 9 preferably, but not necessarily, in a manner such as to preserve the element spacing equal. The staggering should, of course, be such as to prevent short-circuiting of the elements or dipoles The 10 elements may be staggered only in the vertical plane of propagation l3, or alternatively, they may be staggered, obliquely, that is, in both the plane of propagation l4 and the wave front plane l3.

More specifically, considering the embodiment of Figs. 3, 4 and 5, the elements 9 are arranged in six vertical rows IS in the wave front plane l3, four vertical rows IS in .the propagation plane I and five horizontal tiers I1, the corresponding adjacentelements .5, Fig. 4, in each tier being positioned exactly in back of one another. Referrin to Fig. 6, which is a side view, corresponding to Fig. 4, of another embodiment, the dielectric medium 8 has the same volume, X, Y and Z, as the medium of Fig. 3. In the propagation plane I, Fig. 6, the elements 9 in each vertical row It are staggered relative to the elements in the two adjacent vertical rows l8, the spacing between the elements 9 being the same as in the embodiment of Fig. 4, whereby the total number of vertical rows i8 spaced in the propagation plane I, that is, spaced along the depth or thickness dimension Z, is greater than the number of rows IS in the embodiment of Fig. 4. Accordingly, for the same volume, X, Y, Z, the embodiment of Fig. 6 contains a larger number of elements per unit volume, so that the refractive index of this staggered embodiment is greater than that of the linearly-spaced embodiment of Figs. 3, 4 and 5. In Fig. 5, the dotted elements denoted by reference numerals 19 represent the positions of a few typical staggered elements when staggering only in the propagation plane H is utilized; and the dotted lines 20 illustrate the positions of a few typical staggered elements when staggering in both the wave front plane l3 and the propagation plane I4 is employed. In this connection it may be pointed out that the structure of Fig. 3 should be sharply distinguished from the grid structures illustrated by Figs. 3 and 5 of my concurrently filed copending application for Transmission Systems, Serial No. 748,448, filed on May 16, 1947. In the embodiment of Fig. 3 the element spacing in the horizontal or magnetic (H) plane may be greater than a. half wavelength whereby reflection of wave components at the surfaces or faces of the structure does not occur. In the grid structures of my copending application the H-plane spacing is less than a half wavelength so that the horizontal grid strips reflect certain portions of the E components, the unrefiected portions of the E components being propagated through the structure only along the spaces between the grid strips.

Inasmuch as the elements 9, Fig. 3, are linear, the structure operates to delay waves having a polarization, or a polarization component, parallel to the vector II and a propagation direction having a horizontal component such as direction l2. The elements 9 may, however, have any other configuration or'shape and, in particular, F

they may be spherical or circularand fiat, that is, disk-shape d. As stated previously, a structure It comprising spherical elements, resembling ball bearings, is truly isotropic since it functions to delay equally waves having any E polarization and any propagation direction incoming to the structure. On the other hand, in a structure comprising metallic disks positioned so that their flat faces extend parallel to the incoming wave front, the optimum delay action is obtained when the incoming wave propagation direction is perpendicular, and the incoming wave front plane is parallel, to the faces of the disks. The disk structure may be considered as quasiisotropic, since it functions to delay equally all E polarizations in the aforesaid wave front plane.

Referring to Figs. 7, 8 and 9 the polarizability, to of a perfectly conducting sphere will now be determined. In Figs. 7 and 9 reference numeral 2| denotes an originally uniform electric field such as that represented by the electric or E vector ll, Fig. 3. and numeral 22 designates a perfectly conducting sphere immersed in the field 2 I. Now

V=-Ey==-Er cos (36) where V- is the potential of the field 2! y is the ordinate parallel to the E vector.

The free charges on the sphere are displaced by the applied field and it thereby becomes an electric dipole having a moment Me which we wish to determine. In Fig. 7, the electric lines of force enter and pass through the sphere, whereby positive charges appear on one side and negative charges appear on the opposite side, as in Fig. 2, and an electric dipole is simulated. The electric potential, Vout, external to or outside the sphere, is the sum of the applied potential, Va, and the dipole potential, Va, that is vout=Vs+Vd (37) and from Equations 9 and 36 we have V..,.= -Er cos a+ as For the potential Vm, inside the sphere, we have because the sphere 22 is conducting.

As explained on page 73 of the textbook Electromagnetic Waves" by S. A. Schelkunoif, at a bolmdary between two dielectrics, there are two requirements, namely,

Ehngential (inside) =Etangentinl (outside) (40) and cEnormal (inside) =1Enormal (outside) (41) Also. as explained on page 19 of the textbook Static and Dynamic Electricity by Smythe, the above two requirements may be expressed in termsof the potentialas Vin=vcut (42) il ont ln 7 aw where d is the derivative in is the normal direction to the surface.

But since the conducting element 22 is a sphere.

r==a, the radius of the sphere, so that from Equaand ac=41rcod' (48) Substituting in Equation 30, we may obtain the refractive index of a structure In, Fig. 3, comprising spherical elements 22. Thus, for a separation S between elements sufficient to render the mutual coupling effects negligible, we have 1+41rNa' (50) where N is the number of spheres per unit volume of the structure. and n is the refractive index.

In deriving Equations 48 and 50 for a structure comprising perfectly conducting spheres the presence of only an electric field was assumed. In other words the magnetic field, which is inherently coupled to the electric field of an electromagnetic wave was disregarded. Actually, the magnetic field is distorted by the sphere; and this distorted magnetic field tends to reduce the value of the refractive index as given by Equation 50. More particularly, the electric vectors of the super-short wave (microwave) terminate on the conducting sphere, and the electric field is thus perturbed. These electric vectors induce eddy currentsonlthamrfacenf the conducting .wgphgre which prevent the H or magnetic lines of .force frfirh' penetrating the'surface of the sphere. 85 is a resultrtl'ie magnetic linesare' perturbed and circumvent the sphere. Thus, as shown in Figs. 7 and 9 the electric vectors ll terminate on the conducting sphere 22 and the electric field is perturbed; and, in addition, as shown in Figs. 8 and 9, the vectors 24 circumvent sphere 22 and the magnetic field 23 is perturbed.

Now, a conductive sphere 22 immersed in a magnetic field 23 is analogous to a dielectric sphere, that is, a theoretical sphere having a zero dielectric constant, immersed in an electric field. The dielectric sphere has an electric dipole moment, Ms, which we shall now determine and which corresponds in a sense to the magnetic dipole moment of the conducting sphere.

Thus, for the dielectric sphere Vin- 0 (51 and is unknown, because the sphere is not conducting. But. as stated above, for the dielectric sphere m=0 (52) and aut=eo (53) Accordingly, Equations 38 and 43 may be conveniently utilized to determine Mz- Thus LMHHN 13 but :1 1 2 we; --a (58) and since wehave M, --Em0 (61) M:=2noG'E (62) Hence, from Equations (23) and (62) we have u==-21ra (63) As shown by Equation 63, the electric polarizability dz of a sphere having a zero dielectric constant is negative and equal to one-half the value of the polarizability (1c of the conducting sphere, as given by Equation 48. Similarly, at superhigh frequencies, the conducting sphere possesses a. negative magnetic polarizability and the effective permeability of the medium comprising conducting spheres will be altered.

To recapitulate, for the conductive sphere, the inside potential Vm is zero and the inside dielectric constant am is not zero, so that Equation 42 rather than Equation 43 was utilized in conjunction with Equation 38 in determining its polarizability do. On the other hand, for the dielectric sphere, the inside potential Vin is not zero and the inside dielectric constant sin is zero, so that Equation 43 rather than Equation 42 is employed in conjunction with Equation 38 in ascertaining its polarizability dz.

The equation for the relative permeability, [Li'- of a conducting element is similar to Equation 30 for the relative dielectric constant, er, of the element, that is.

[tr is the relative permeability to is the permeability in free space a, is the magnetic polarizability. For a spherical element, we have ;l.r=1--2irNl1 which is analogous to Equation 49.

Now, from Equations 30, 34, 50 and 65 we have for the conducting sphere It may be interpolated here that the focussing action of the fast, metallic-advance, lens comprising dielectric channels and disclosed in my copending application mentioned above, Serial No. 642,723, filed January 22, 1946, may be attributed to polarization effects. In the fast channel lens, the electric lines of force entering the channels are forced to assume the sinusoidal distribution in accordance with the dominant mode. Hence these lines of force are perturbed by the metallic walls in substantially the same manner as they would be perturbed by spheres each having a zero dielectric constant. The polarizability is negative so that now, if

where q is the H-plane or "a dimension of the dielectric channel and if we have and 85 A 2 1 74 n a 2g which corresponds to the equation for the refractive index, as given in the copending application just mentioned.

As previously discussed, the magnetic field perturbance, produced at high frequencies by the eddy current effect may be substantially eliminated by shapingt "e elements so that the magnetigjnesiareiiotlpertuiibed. More specifically, each elementmaybe' shape'cl' so as to have a neg-5 nwk 11141. 3!imnenijinnthwinter.ion. e1;- wave pro 'glgi gn and, in the direction of the elec'tri'c'field, the same dimension as in the sphere. Thus, referring to Fig. 9, reference numeral 25 denotes a conducting circular disk having its flat faces parallel to the E vector i I and the H vector 24. Now the torque, T, on a flat disk having a radius, B. may be expressed as 3 T=[ (E sin 0)][E cos 0] (75 where R is the radius of the disk.

The first bracket represents the dipole moment, the second field: and the product is the torque. For the disk 25 having its plane or face parallel to E where can: is the electric polarizability of the disk. Hence, from Equation 30, neglecting mutual eifects, we have n=1+- NR'=ef The refractive index, n, for the array of disks, as given by Equation 79 is independent of the magnetic field, as already indicated.

Referring to Figs. and 11, reference numerals 25 denote forty-seven conductive spherical elements resembling marbles, or pellets, and mounted on vertical wooden dowels or rungs 21, the rungs 21 being supported by the wooden base member 28. The pellets are dispersed or spaced along the three axes or directions, X, Y, and Z in the air dielectric medium 29 and in a manner such as to form an electromagnetic delay array 39. More particularly, the medium 29 and the array 30 together constitute a delay structure or prism 3| having a front face 33 and an inclined back face 33. The pellets 26 are grouped in three vertical panels, namely, a front panel 34 comprising twenty-five pellets, an intermediate panel 35 comprising twelve pellets and a back panel 36 comprising ten pellets. The front panel 34 comprises five horizontal tiers 31 each having five pellets, the middle panel comprises three horizontal tiers 38 each having four pellets and the back panel 36 comprises two horizontal tiers 39 each having five pellets. Considered differently, the front panel 34 comprises five verticals or stacks 40 each having five pellets, the middle panel 35 comprises four vertical stacks 4| each having three pellets and the back panel 36 comprises five stacks 42 each having two pellets. As is apparent from the drawing, the front and back panels 34, 36 are aligned; and the intermediate panel 35 is obliquely, that is, vertically and horizontally, staggered relative to the two outer panels 34, 36. Thus, as shown by the dotted lines 43, Fig. 10, the corresponding stacks 49, 42 in the front and back panels 34, 36 are horizontally aligned and, as shown by the dotted lines 44. Fig. 11, the two tiers 39 of the back panel 36 are aligned with the two bottom tiers 3B of the front panel 34, whereby each pellet 26 in the back panel 35 occupies a position in the medium 29 corresponding, in the vertical and horizontal planes, to that occupied by a pellet in the front panel 34. Each tier 38, Fig. 11, of the middle panel 35. is positioned mid-way between two adiacent tiers 31 of the front panel 34; and each stack 4| of the middle panel 35 is positioned mid-way between the lines 43 connecting the corresponding stacks 43, 42 of the front and back panels 34, 35. The center-to-center spacings, S, between each pellet and the pellets adjacent thereto are substantially equal.

As explained above, the electric polarizability a of each sphere or pellet is directly proportional to the cube of the radius of the pellet and, assuming the radius a is given and the mutual effects are negligible, 0. may be ascertained from Equation 50 or 62. With a determined and the desired index of refraction n selected, 11. being greater than unity as, for example, 1.36, the number N of pellets per unit volume of the prism and hence the center-to-center spacing S for the pellets of known radius a may be ascertained. Conversely, with a and N, and therefore S, selected, the theoretical value of n may be ascertained. In this connection it should be noted that, while the total number of pellets in the prism of Figs. 10 and 11 is forty-seven, the prism may contain a difierent number of pellets, and the prism may have any practical total volume. Moreover, the number of pellets in each panel, or tier. or in each stack, may of course be considerably different from the number illustrated, provided that the desired optical configuration for the structure is preserved. By way of illustration, assuming the diameter of each pellet is three-eighths of an inch and the center-to-center spacing S is equal to three-quarters of an inch, N equals about 2.38. Also, while the dielectric medium is air, the medium may of course be any other dielectric substance. Again, if desired, the entire structure may be enclosed in an evacuated container, and the medium may be the enclosed vacuum.

In operation, Figs. 10 and 11, waves having a propagation direction l2 and an electric polarization ll, 8r any other polarization in the plane of the wave front I3 are propagated through the prism 3| and, since the refractive index is greater than unity, the phase velocities of the wave components passing through the thicker portion of the prism are delayed a greater amount than the phase velocities of the components passing through the thinner portion, with the result that the propagation direction of the wave front is bent toward the thicker portion, as in an optical lens, and the emerging outgoing direction 45 is at an angle to the incoming direction l2.

Referring to Figs. 12 and 13, reference numeral 30 designates a metallic delay array, or artificial dielectric material, which comprises, as in the array 30 of Fig. 10, conductive pellets 26 dispersed along the X, Y and Z axes in the air dielectric medium 29. The array 30 comprises fifty pellets and is shaped so as to form a plano-convex circularly symmetrical delay lens 50 having a front fiat face 5| and a back convex face 52, an optical axis 53 and a point focus 54. The refractive index, n, of the lens 50 is greater than unity and may be determined in the manner explained above in connection with the prism 3|. For example, the index of the lens 50 may be the same as that of the prism 3|. Numeral 55 denotes a point type primary antenna, such as a conical horn, having its orifice coincident with the point focus 54 of the lens. The horn is connected by a dielectric guide 56 to a radio translation device 51, such as a microwave transmitter, receiver or radar transceiver.

More specifically, the pellets of the lens 50 are grouped in three panels 34, 35 and 36, the front, middle and back panels 34, 35 and 33 comprising respectively, twenty-five, sixteen and nine pellets. The front panel 34 is the same as the front panel 34 of the prism 3|, Fig. 10, and comprises five tiers 31 of five pellets each, or five stacks 40 of five pellets each. The middle panels 35 of the lens 50 comprises four tiers 38 of four pellets each, or four stacks 4| of four pellets each. The back panel 35 comprises three tiers 39 of three pellets each or three stacks 42 of three pellets each. Since the lens 50 is not of solid construction the faces 5| and 52, shown in dot-dash lines, are not physical surfaces but are in a sense, optical surfaces. Also, while the diameter or aperture 58 of the lens 50 is such that the front and back faces 5|, 52 do not intersect any of the pellets, the aperture 58 may be smaller than shown and such that the corresponding convex face, illustrated by the dotted line 59, and one or more outer pellets intersect, so that a portion of each intersected pellet lies outside the lens and the remaining portion is included in the lens. In this event, the pellet portions external to the lens should be removed, in order to secure the desired optical contour. In other words,

the lens may comprise only whole pellets, or both.

whole and fractional pellets.

The equation for the convex contour of the back face 52 will now be determined. In Fig. 13,

the reference letter A denotes the phase length of the path traversed by a wavelet r ray emitted at the focus 84 and propagated through the thick vertex portion of the lens and along the lens axis 53 to the flat front face II. Reference letter B denotes the phase length of the path traversed by a ray emanating from the focus 54 and propagated to the periphery so as to just avoid the lens and reach the front face SI. In order to convert the spherical wave front 60 originatin at the focus 84 into a plane wave front 8| at the front face A and B must be equal.

Now

f is the focal length of the lens,

a: is the lens thickness along the axis 03,

1 is the radius or half-aperture of the lens,

0 is the phase velocity in the lens, as before, and no is the phase velocity in free space.

Hence,

I V (f+ )+y (82) o a v or, since where n is the refractive index we have (n=-1):c +2ja:(n1)y*=0 (84) which is the equation for a hyperbola.

In operation, Figs. 12 and 13, assuming the device 51 is a transmitter, energy is supplied by the transmitter 81 over guide 58 to the horn 55 and a wave having a polarization I I and a spherical wave front is propagated towards the lens 50. The phase of the wave components passing through the thick central of vertex portion of the lens are retarded a greater amount than the phase of the wavelets propagated through the outer thinner lens portion. and the wavelets arriving at the front face SI are cophasal. Stated differently, an outgoing spherical wave front 80 is converted by the lens to a plane front I extending perpendicular to the axis I8. In rece tion, the converse operation sndanincaa iasml e havin .apm

ation direc rallel to the E53 is t ransnmailquama -view lens into a spherical wave.fioiiijj pgifieggingknjthe "focus 84. In other words, the incoming parallel rays 62, 88 are bent or refracted by the lens, as illustrated by the rays 84, 85 and focussed on the primary antenna 55. Inasmuch as the lens 50 is circularly symmetrical, focussing action is obtained in all planes containing the optical axis 83. Also, since the elements 26 are spherical the lens 80 is isotropic. In practice, a lens constructed in accordance with Figs. 12 and 13 and comprising pellets having diameters of three-eighths of an inch and spaced center-to-center threequarters of an inch operated in a highly satisfactory manner.

The piano-convex lens of Figs. 14 and 15 is the same as the lens of Figs. 12 and 13 except that polystyrene foam having a dielectric constant of 1.014, that is, substantially unity, and

a refractive index of 1.007, also substantially unity, is utilized in place of air as the dielectric medium. In Figs. 14 and 15, reference numerals II, I2 and I3 denote three thick polystyrene foam slabs in which the pellets 26 of panels 84, 35 and 36 are embedded, respectively. Numerals I4 and I5 denote two thin polystyrene foam spacer sheets included, respectively, between slabs II and I2 and slabs I2 and I3. The panels 34, 35 and I6 constituting the metallic delay lens I0 are substantially the same as the panels 84, 35 and 38 of the lens 50. The operation of the system of Figs. 14 and 15 is substantially the same as that of Figs. 12 and 13. In one embodiment of the invention, constructed in accordance with Figs. 14 and 15 and successfully tested, the pellets 28 were three-eighths of an inch in diameter and spaced center-to-center three-quarters of an inch.

Referring to Figs. 16, 17 and 18, reference numeral denotes a quasi-isotropic, circularly symmetrical, delay lens comprising a dielectric medium 8| having a dielectric constant of unity, substantially, and a metallic delay array 82 immersed therein. The dielectric medium 8| comprises five closely adjacent circular slabs 83, 84, 85, 80 and 81 of polystyrene foam and the negligible air dielectric 88 between the adjacent parallel slabs. Numerals 89, 90, 9|, 92 and 93 denote the front surfaces, and numerals 94, 95, 98, 81 and designate the back surfaces, of the slabs 88, 84, 85, 86 and 81, respectively. The slabs are coaxially supported on the wooden cross-member or rung 99, the wooden uprights I00 and the wooden base member 28. The metallic delay array 82 comprises a large number of copper foil disks IOI having negligible thickness and mountediinthe back surfaces of the five slabs, and on the front surface of slab 83, in a manner such that the conductive disks are uniformly dispersed along three dimensions in the medium 8|. Hence the front and back faces, and the diametral dimension of each disk IOI, extend parallel to the wave front I3 which contains the electric vector II. Considered differently, the metallic delay structure comprises six circular metallic panels I02, I08, I04, I05, I08 and I01 spaced equally along the optical axis 53 of the lens 80 and comprising different pluralities of metallic disks I0l. Each panel contains whole and fractional disks. The disks MI in panels I03, I05 and I01 are obliquely staggered relative to the disks III in panels I02, I04, and I06. Numerals I08 denote polystyrene foam spacers mounted on the rung 99 between the slabs and adjacent the outer slabs, and preferably dimensioned so that the center-to-center spacings S of the adjacent disks in the adjacent panels and the center-to-center spacings S of the adjacent disks in each panel are equal. If desired, the spacers I08 may be omitted and the slabs 83 to 81 may each have a thickness such as to render the slabs contiguous, whereby the air spacing between slabs is eliminated, substantially. The diameters of the slabs, and hence of the panels, are progressively stepped in conformity with the piano-convex shape of the lens.

As already discussed, the electric polarizability can! of each disk IN is directly proportional to the cube of the radius R of the disk and, assuming the radius is given. may be ascertained from Equation '18. With aetermin dj the radius R aidthe desired index of refraction n selected, the number N of disks per unit volume of the metallic lens 80. and hence the 'one'si'de of each of many center-to-center spacing, S, of the disks may be determined from Equation 79, assuming mutual elfects are disregarded, or from Equations 31 and 78 if the mutual effects are considered. Conversely, with R and N, and therefore S, selected, the theoretical value of 11 may be ascertained. The operation of the disk lens of Figs. 16, 17 and 18 is essentially the same as that of the lens of Fig. 12 or Fig. 14. The lens 30 is, however, isotropic only for waves having a propagation direction parallel to the axis 53 whereas, as stated above, the lens 50 and the lens 10 are each truly isotropic. As in the lenses 50 and 10, focussing obtains in all axial planes of the lens 80 and a pencil or point type beam is produced.

As shown by Fig. 19. in which reference numeral I I denotes the measured E-plane directive pattern for an antenna system constructed in accordance with Figs. 16, 17 and 18, the directive action of the small delay lens 80 is highly satisfactory. In the tested system just mentioned, the lens diameter or aperture, the disk radius R and t h e d isk spacing S were, respectively twenty-four inches, flve-sixteenths of an inch, andmeinch; and the pattern was measured at a design wavelength of x equal to 1.2 5

centimeters, The pattern IIO comprises a single major IoBe I II, the two vestigial lobes H2 and the minor lobes II3. As is desired, the vestigial and minor lobes are considerably below the peak of the major lobe, the vestigial lobes being 15 decibels and the minor lobes being 20-25 decibels down from the peak. The relative intensity of the minor lobes is, in general, more satisfactory than obtained in prior art reflective antenna structures. The half-power width II 4 of the major lobe is 7.6 degrees. This beam or lobe width is dependent upon several factors including the focussing action of the lens, and it is also directly proportional to the lens aperture. The 7.6 degrees beam width for the lens of the invention is comparable to the beam widths of other prior art passive antenna members, such as parabolic reflectors, zone plate and other lenses, having two-foot apertures. It may be observed that, as disclosed in my companion application, a polarized metallic delay strip lens having a six-foot aperture has a half-power beam width of only 2.68 degrees. Hence, the beam width of a lens constructed in accordance with Figs. 16, 17 and 18 and having a six-foot aperture would be about 2.68 degrees.

/ In P a est ananelsnfthelens 80 a efi gnstructe '7 lns vidually applying oifj'nounting the copper foil or r l fi i igd s sspnftliera istyrenefslgis. A delay lens of the disk type may,

however, be more easily and simply constructed by raying conductive material, such as paint, on

thin solid dielectric sheets through a thin sheet-metal master plate perforated with small or square ls of proper size. A circular during the spraying process, between the plate and the sheet in order to obtain a circular panel of spaced conductive dots or motes." The size or diameters of the various masks are graded in a manner such that the desired convex lens contour is secured when the sheets are stacked or assembled to form the delay structure. In the assembled lens the sheets are bolted together and solid diqL cmc uondensn g s may or mavlnoabe Figs. 20, 21, 22 and 23 illustrate a painted disk or dot lens constructed as just described. In more detail, reference numeral I20 designates a quasi-isotropic, circularly symmetrical, delay lens comprising four solid dielectric spacer sheets I23, I25, I21 and I29 and five solid dielectric panel sheets I22, I24, I26, I28 and I30. Reference numerals I32, I33, I34, I and I36 denote circular panels painted on the panel sheets I22, I24, I26, I28 and I30, respectively, and having graded diameters tapering from a maximum for panel I32 to a minimum for panel I36 in conformity with the convex hyperbolic optical face 52 of the lens I20. The panels comprise difierent pluralities of square dot es or moteg lgl of conductive paint, and are not staggered. The adjacent motes I31 of each panel'efi spaced a distanges; and the thicknesses of the panel and spacer sheets are selected such that the corresponding motes in adjacent panels are spaced a distance S. The panel and spacer sheets, assembled as shown in Fig. 20, are held securely together by the wooden frame members I2I and the nut and bolt assemblies I3I. The panel and spacer sheets may be ,composed of polystyrene foam or other suitable dielectric material such as cellophane. If the material is transparent, the motes I31 produce a shading effect, as shown in Fig. 21, which decreases in all radial directions from a maximum intensity at the center of the lens to a minimum at the periphery, by reason of the circular symmetry of the lens.

The electric polarizability a of the individual square mote having a side length 2R is not substantially different from the polarizability a of a circular mote having a radius R. Hence with the side half-length R (or radius R) given, the p01arizability a may be ascertained from Equation 78, as in the lens of Fig. 16. With a. determined and R known, the desired refractive index 11 greater than unity may be obtained by properly selecting N and S in accordance with Equation 79. The quasi-optical and electrical operation of the system of Fig. 20 is substantially the same as that of the system of Fig. 16.

Referring to Figs. 24 and 25, the metallic delay painted disk lens I40 is substantially the same as the painted lens I20 of Figs. 20, 21, 22 and 23, except that the lens I40 is cylindrically symmetrical and has a line focus I4I, whereas the lens I20 is circularly symmetrical and has a point focus 54. The front face 5| of the lens I40 is cylindrically convex and the back face 52 is fiat. The lens I40, Figs. 24 and 25, comprises five polystyrene foam rectangular slabs I42, I43, I44, I45 and I46 and the five conductive panels I41, I48, I49, I50 and I5I, sprayed on the aforesaid slabs. respectively. The panels are not staggered and they have equal lengths but graded widths. As in the lens of Fig. 20, the motes I31 are of conductive paint. The slab thicknesses are such that the spacings s between adjacent motes I37 and along the three dimensions X, Y and Z of the structure, are equal. Numeral I52 denotes a sectoral horn connected to guide 56 and device 51 and having its long mouth aperture I53 aligned with the focal lens I of the lens I40.

The mote polarizability a, the mote side halflength R, the number N of motes per unit volume of the structure, the spacing s between motes and the refractive index n are the same as in the lens of Fig. 20. In operation, the sectoral horn energizes the focal line I and the lens delays the inner rays passing through the thicker lens portion relative to the outer rays. Hence the cylindrical wave front emerging from the horn mouth aperture I52 and aligned with the line focus I is transformed by the lens III to a plane wave. In other words, the lens focusses the waves in the E or vertical plane containing the electric polarization II but does not focus in the H or horizontal plane. Accordingly, a fan beam is produced having a small width in the E-plane and a large width in the H-plane. If desired, a point beam may be secured by properly inserting a lens in the horn mouth aperture I52, as is well known.

As already stated, the E dimension, that is. the dimension as measured in a direction parallel to the electric wave polarization, of each conductive element in the structures described thus far is relatively small compared to a half wavelength, and therefore such as to avoid resonant eifects. Moreover, the structures illustrated by Figs. 3, 10, 12, 14, 16, 20 and 24 have a relatively broad band with, since the frequency bands or regions in which they are ordinarily used are sufficiently remote, from the region of anomalous dispersion,

that the effective dielectric constant and the refractive index do not vary appreciably with frequency. To illustrate, in a tested system comprising elements having an E dimension corre sponding to a quarter wavelength at i to 7.6 centimeters (3,947.3 megacycles) the index of refraction n varied from 1.41 at i=8 centimeters (3,750 megacycles) to 1.43 for i=7 centimeters (4,285.7 megacycles). In other words, the index 11 increased only 0.02 as the wavelength decreased one centimeter, that is, as the frequency increased 535.7 megacycles. As the frequency increases from 4,285.7 megacycles, the index 1|. increases until at centimeters corresponding to 7,894.6 megacycles the metallic structure is opaque and the index n is very high. At this wavelength the E dimension of the elements is a half wavelength, whereby resonant efiects occur and the artificial dielectric or metallic structure acts like an ordinary solid dielectric substance near its region of anomalous dispersion. At the lower wavelengths, that is, higher frequencies, the metallic structure appears to have an index of refraction less than unity. With the index 11. less than unity, the phase velocity of the waves propagated therethrough is accelerated rather than retarded, and the refractor becomes a fast metallic advance refractor. To continue, linear elements or rods p0- sitioned parallel to the E vector and having an E dimension or length of a half wavelength have a very broad resonance band, and the region or range of anomalous dispersion in a metallic artiflcial dielectric structure comprising such rods is very large. This region, or frequency band, may be considerably reduced by tilting the half wave rods in the wave front plane, so that they are more nearly perpendicular to the electric (E) vector, whereby the rods become loosely coupled to the moving field and acquire a higher "62. The rods should be unsymmetrically or dissimilarly tilted in order to insure a rapid decrease in the radiation damping, and hence a sharp resonant characteristic, and to minimize radiation from the array of rods. symmetrically tilting the rods would result in maximum radiation from the array of a wave polarized parallel to the rods.

Referring now to Figs. 26, 27 and 28. reference numeral I 60 denotes a frequency-sensitive metallic artificial dielectric structin-e comprising a plurality of resonant 1 u on. each a half wavelength long a given frequency and disposed in four vertical panels 162, I02, I and I05. Considered differently, the rods I are arranged in ten horizontal tiers I66. The adiacent rods Iii in each panel areoppositely tilted. The corresponding rods I61 in each tier are embedded in the same polystyrene foam horizontal slab I61, as illustrated, the thickness or vertical height of each slab being approximately the same as the vertical projection"Lv" of the rod length "L." Numerals I denote polystyrene spacer slabs each of which is positioned between a different pair of adjacent tier slabs I61. As shown in more detail in Fig. 27, the rod tilt is such that the center-to-centerhorizontal spacing Bx of the rods is about three times the vertical center-to-center spacing 8,. of the rods, and the horizontal rod spacing Se is about one half the horizontal S4 spacing, the spacings S, being preferably less than one quarter of the aforesaid given wavelength. As shown by Fig. 28, assuming the structure I" is used as a lens, the front face It! of the structure I" is circular and flat. The back face is circularly convex 0r circularly concave, as shown by the dot-dash lines I10 and "I, Fig. 26. dependent upon the operating frequency of the translation device I12. The device I12 includes means for varying the operating frequency or is designed so that the frequency may be easily altered.

In operation, Fig. 26, assuming the operating frequency of device I12 is higher than any of the frequencies included in the anomalous dispersion region for the structure I", the dielectric constant and refractive index of the structure are each less than unity and the phase velocity, v, of the waves in the lens I" is greater than the phase velocity, D0. of free space. Accordingly. the back face of the lens I" is made ellipsoidally concave, in accordance with the disclosure in my aforesaid copending application Serial No. 642,723. On the other hand, if the frequency of device I12 is lower than any of the frequencies in the anomalous dispersion region, the dielectric constant and refractive index of the structure are each greater than unity and the phase velocity, v, of the waves in the lens I is smaller than the free space phase velocity, 170. Accordingly, in this case, the back face is hyperbolically convex. as in the structure illustrated, for example. by Fig. 13. In either case the lens I" functions to focus the waves in all planes containing the lens axis 52, as already explained.

Referring to Fig. 29, reference number I12 denotes a measured dispersion curve of a metallic structure constructed in accordance with Figs. 26, 27 and 28 and in which L, In, S, S, and S; were respectively 1.25 inches, 0.25 inch, 1.5 inches. 0.5 inch and 0.75 inch. In the test, the operating wavelength was 7.6 centimeters. As shown by curve I13 the re ion of anomalous dispersion for the tested metallic structure I" occurs when the rods I6I are approximately a half wavelength long. In other words. the curve shows that the structure is resonant at a frequency of about 3,947 megacycles, and at this frequency the 1.25 inch, or 3.175 centimeter, rods are almost a half wavelength long since 3,947 megacycles correspond to 7.60 centimeters. Thus, it is seen that the structure I" has an anomalous dispersion region analogous to that of a solid dielectric refractor. Because of the rapid change of the refractive index a with frequency, the artificial di- 23 electric "I may be utilized, in prisms or variable focal length lenses, as a means for separating narrow channels. Also, as will be disclosed and claimed in my last-mentioned proposed application, if desired, a slow lens in accordance with Fig. 16, for example, may be combined with the fast dielectric channel lens of my copendin application, Serial No. 642,723, to secure a compound achromatic metallic fast-slow lens.

Although the invention has been described in connection with certain embodiments, it is to be understood that it is not to be limited to the embodiments described inasmuch as other apparatus may be successfully employed in practicing the invention.

What is claimed is:

1. A piano-convex metallic lens for retracting a radio wave comprising flat circular conductive disks mounted on solid dielectric members and spaced along three directions in said lens, the flat faces of said disks being parallel to the electric polarization of said wave, said disks having equal diameters each less than one-half of the wavelength of said wave.

2. A piano-convex, circularly symmetrical, lens for refracting a radio wave having a given wavelength, said lens comprising circular polystyrene ioam slabs extending parallel to each other, a plurality of metallic disks mounted on each slab, the spacing between adjacent slabs and between adjacent disks on the same slab being less than the wavelength of said wave and the diameter of each disk being less than onehaif of said wavelength.

3. A device for retracting electromagnetic waves. the wavelength of which is within a predetermined range of wavelengths, said device comprising a plurality of arrays of conductive elements said elements being substantially alike and having a maximum dimension which is small with respect to the wavelength of the median frequency of said range of wavelengths, each of said arrays comprising a plurality of said conductive elements substantially uniformly distributed over the entire surface of a plane area, the major dimensions of said area being large with respect to said maximum element dimension, the spacings between adjacent elements not exceeding three times the said maximum dimen- 24 sion of said elements, said plurality of arrays being placed with their respective planes parallel to each other along a common axis perpendicular to said planes, the spacings between the planes of adjacent arrays being substantially the same as the inter-element spacings of the arrays.

4. The device of claim 3 in which contour lines defined by the outermost edges of the outermost elements of the plurality of arrays of elements are substantially those of a piano-convex lens.

5. The device of claim 3 in which the conducting elements are circular disks.

6. The device of claim 3 in which the conducting elements are spheres.

7. The device of claim 3 in which the conducting elements are short pieces of rod.

8. The device of claim 3 in which the contour lines defined by the outermost edges of the outermost elements of the plurality of arrays of elements are those of a simple type of optical retractor. I

WINSTON E. KOCK.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 706,739 Fessenden Aug. 12, 1902 2,288,735 O'Connell July 7, 1942 2,298,272 Barrow Oct. 13, 1942 2,317,464 Katzin Apr. 27, 1943 2,403,657 Harvey July 9, 1946 2,415,352 Iams Feb. 4, 1947 2,415,807 Barrow et al. Feb. 18, 1947 2,423,648 Hansell July 8, 1947 2,464,269 Smith Mar. 15, 1949 FOREIGN PATENTS Number Country Date 327,312 France June 19, 1903 587,771 Germany Nov. 8, 1933 OTHER REFERENCES Electronic Industries, March 1946, page 66.

Electronica, March 1946, pa e 101.

Bell Telegraph System publication, Mon0- graph B. 1423. 

